Fuzzy Hypothesis Testing for Radar Detection: A Statistical Approach for Reducing False Alarm and Miss Probabilities

This paper addresses a fundamental challenge in statistical radar detection systems: optimizing the trade-off between the probability of a false alarm ($P_{FA}$) and the probability of a miss ($P_M$). These two metrics are inversely related and critical for performance evaluation. Traditional detection approaches often enhance one aspect at the expense of the other, limiting their practical applicability. To overcome this limitation, a fuzzy hypothesis testing framework is introduced that improves decision making under uncertainty by incorporating both crisp and fuzzy data representations. The methodology is divided into three phases. In the first phase, we reduce the probability of false alarm $P_{FA}$ while maintaining a constant probability of miss $P_M$ using crisp data characterized by deterministic values and classical statistical thresholds. In the second phase, the inverse scenario is considered: minimizing $P_M$ while keeping $P_{FA}$ fixed. This is achieved through parameter tuning and refined threshold calibration. In the third phase, a strategy is developed to simultaneously enhance both $P_{FA}$ and $P_M$, despite their inverse correlation, by adopting adaptive decision rules. To further strengthen system adaptability, fuzzy data are introduced, which effectively model imprecision and ambiguity. This enhances robustness, particularly in scenarios where rapid and accurate classification is essential. The proposed methods are validated through both real and synthetic simulations of radar measurements, demonstrating their ability to enhance detection reliability across diverse conditions. The findings confirm the applicability of fuzzy hypothesis testing for modern radar systems in both civilian and military contexts, providing a statistically sound and operationally applicable approach for reducing detection errors and optimizing system performance.